{"text_format":"3","workbook":"xlsx","n_sheets":4,"sheets":["y' agrees","y' and y\" agree","Sheet3","Sheet4"],"not_rendered":{"charts":2,"images":2,"defined_names":7,"comments":2},"read":"whole","date_system":"1900"}

{"sheet":"y' agrees","index":0,"n_rows":53,"n_cols":6,"rows_kept":53,"merged":[[46,2,46,4]]}
[null,"            Cubic Splines","     Cubic Splines"]
[null," When y' Agrees at Nodes"]
[]
[null,"            This DIGMath module illustrates "]
[null,"           the notion of using cubic splines"]
[null," to create a smooth curve made up of a series"]
[null,"      of cubic curves that will pass through"]
[null,"     any set of points and where the slopes"]
[null,"   agree at the points where the cubics meet."]
[]
[]
["How many points (3 - 19)?",{"$nulls":3},{"$f":"2*F12+5","v":15},5]
[]
["Enter the coordinates in the cells below:"]
["    with the x's in ASCENDING order:"]
[null,"x","y"]
[1,0,4,1]
[2,2,9,2]
[{"$f":"IF(A18<n,A18+1,\"\")","v":3},4,16,3]
[4,7,18,4]
[5,9,12,5]
[6,12,8,6]
[7,15,16,7]
[8,17,22,8]
[9,20,6,9]
[10,23,3,10]
[11,25,11,11]
[12,28,13,12]
[13,30,8,13]
[14,32,1,14]
[15,35,5,15]
["",37,15,16]
["",40,25,17]
["",42,28,18]
["",44,11,19]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[{"$nulls":3},"   Item 1"]
[{"$nulls":3},"   Item 2"]
[{"$nulls":3},"   Item 3"]
[{"$nulls":3},"   Item 4"]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["    Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

{"sheet":"y' and y\" agree","index":1,"n_rows":46,"n_cols":6,"rows_kept":46,"merged":[[39,2,39,4]]}
[null,"            Cubic Splines","        Cubic Splines"]
[null,"When y' and y\" Agree at Nodes"]
[]
[null,"               This DIGMath module illustrates "]
[null,"              the notion of using cubic splines"]
[null,"     to create a smooth curve made up of a series"]
[null,"       of cubic curves that will pass through any"]
[null," set of points and where both the first and second"]
[null,"     derivatives agree where the cubics connect."]
[]
[]
[null,"How many points (4 - 10)?",null,null,{"$f":"F12","v":6},6]
[]
["Enter the coordinates in the cells below:"]
["    with the x's in ASCENDING order:"]
[null,"x","y"]
[1,0,4,1]
[2,1,10,2]
[3,3,18,3]
[{"$f":"IF(A19<nn,A19+1,\"\")","v":4},7,16,4]
[5,9,23,5]
[6,11,22,6]
["",12,35,7]
["",14,47,8]
["",16,66,9]
["",18,88,10]
[]
[]
[]
[]
["Click each item below for suggestions and investigations"]
[{"$nulls":3},"   Item 1  "]
[{"$nulls":3},"   Item 2"]
[{"$nulls":3},"   Item 3"]
[{"$nulls":3},"   Item 4"]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["    Click this link:",null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

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[null,"x","y",null,"First cubic",null,null,"Second cubic",null,null,"Third cubic",null,null,"Fourth cubic",null,null,"Fifth cubic",null,null,"Sixth cubic",null,null,"Seventh cubic",null,null,"Eighth cubic",null,null,"Eighth cubic"]
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[5,{"$f":"IF(A6<=n,'y'' agrees'!B21,\"\")","v":9},{"$f":"'y'' agrees'!C21","v":12},null,"d1 =",{"$f":"$B4-$B2","v":{"v":4,"d":"4.000"}},null,"d1 =",{"$f":"$B6-$B4","v":{"v":5,"d":"5.000"}},null,"d1 =",{"$f":"$B8-$B6","v":{"v":6,"d":"6.000"}},null,"d1 =",{"$f":"$B10-$B8","v":{"v":5,"d":"5.000"}},null,"d1 =",{"$f":"$B12-$B10","v":{"v":5,"d":"5.000"}},null,"d1 =",{"$f":"$B14-$B12","v":{"v":5,"d":"5.000"}},null,"d1 =",{"$f":"$B16-$B14","v":{"v":5,"d":"5.000"}},null,"d1 =",{"$f":"$B18-$B16","v":{"v":0,"d":"0.000"}},null,"d1 =",{"$f":"$B20-$B18","v":{"v":0,"d":"0.000"}}]
[6,{"$f":"IF($A7<=n,'y'' agrees'!B22,LOOKUP(n,A$2:A$20,B$2:B$20))","v":12},{"$f":"IF($A7<=n,'y'' agrees'!C22,LOOKUP(n,A$2:A$20,C$2:C$20))","v":8},null,"dd =",{"$f":"F5^2*F6^2*(F6-F5)","v":{"v":128,"d":"128.000"}},{"$f":"IF(F7=0,\"No Solution\",\"\")","v":""},"dd =",{"$f":"I5^2*I6^2*(I6-I5)","v":{"v":450,"d":"450.000"}},{"$f":"IF(I7=0,\"No Solution\",\"\")","v":""},"dd =",{"$f":"L5^2*L6^2*(L6-L5)","v":{"v":972,"d":"972.000"}},{"$f":"IF(L7=0,\"No Solution\",\"\")","v":""},"dd =",{"$f":"O5^2*O6^2*(O6-O5)","v":{"v":300,"d":"300.000"}},{"$f":"IF(O7=0,\"No Solution\",\"\")","v":""},"dd =",{"$f":"R5^2*R6^2*(R6-R5)","v":{"v":450,"d":"450.000"}},{"$f":"IF(R7=0,\"No Solution\",\"\")","v":""},"dd =",{"$f":"U5^2*U6^2*(U6-U5)","v":{"v":450,"d":"450.000"}},{"$f":"IF(U7=0,\"No Solution\",\"\")","v":""},"dd =",{"$f":"X5^2*X6^2*(X6-X5)","v":{"v":300,"d":"300.000"}},{"$f":"IF(X7=0,\"No Solution\",\"\")","v":""},"dd =",{"$f":"AA5^2*AA6^2*(AA6-AA5)","v":{"v":0,"d":"0.000"}},{"$f":"IF(AA7=0,\"No Solution\",\"\")","v":"No Solution"},"dd =",{"$f":"AD5^2*AD6^2*(AD6-AD5)","v":{"v":0,"d":"0.000"}},{"$f":"IF(AD7=0,\"No Solution\",\"\")","v":"No Solution"}]
[7,{"$f":"IF($A8<=n,'y'' agrees'!B23,LOOKUP(n,A$2:A$20,B$2:B$20))","v":15},{"$f":"IF($A8<=n,'y'' agrees'!C23,LOOKUP(n,A$2:A$20,C$2:C$20))","v":16},null,"e0 =",{"$f":"C3-C2-F2*F5","v":{"v":0,"d":"0.000"}},null,"e0 =",{"$f":"$C5-$C4-I2*I5","v":{"v":-11.5,"d":"-11.500"}},null,"e0 =",{"$f":"$C7-$C6-L2*L5","v":{"v":2.559999999999995,"d":"2.560"}},null,"e0 =",{"$f":"$C9-$C8-O2*O5","v":{"v":-5.6266666666666705,"d":"-5.627"}},null,"e0 =",{"$f":"$C11-$C10-R2*R5","v":{"v":30.339999999999982,"d":"30.340"}},null,"e0 =",{"$f":"$C13-$C12-U2*U5","v":{"v":-1.7733333333333476,"d":"-1.773"}},null,"e0 =",{"$f":"$C15-$C14-X2*X5","v":{"v":2.2785185185185153,"d":"2.279"}},null,"e0 =",{"$f":"$C17-$C16-AA2*AA5","v":{"v":0,"d":"0.000"}},null,"e0 =",{"$f":"$C19-$C18-AD2*AD5","v":{"$error":"#DIV/0!"}}]
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[11,{"$f":"IF($A12<=n,'y'' agrees'!B27,LOOKUP(n,A$2:A$20,B$2:B$20))","v":25},{"$f":"IF($A12<=n,'y'' agrees'!C27,LOOKUP(n,A$2:A$20,C$2:C$20))","v":11}]
[12,{"$f":"IF($A13<=n,'y'' agrees'!B28,LOOKUP(n,A$2:A$20,B$2:B$20))","v":28},{"$f":"IF($A13<=n,'y'' agrees'!C28,LOOKUP(n,A$2:A$20,C$2:C$20))","v":13},null,"coordinates:",null,null,"coordinates:",null,null,"coordinates:",null,null,"coordinates:",null,null,"coordinates:",null,null,"coordinates:",null,null,"coordinates:",null,null,"coordinates:",null,null,"coordinates:"]
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[]
[]
[]
[]
[null,"x","y",null,"First cubic",null,null,"Second cubic",null,null,"Third cubic",null,null,"Fourth cubic",null,null,"Fifth cubic",null,null,"Sixth cubic",null,null,"Seventh cubic",null,null,"Eighth cubic",null,null,"Ninth cubic",null,null,"Tenth cubic"]
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